ECE 145A / 218 C, notes set 1: Transmission Line Properties and Analysis

Transcription

1 class nos, M. Rodwll, copyrighd 9 ECE 145A 18 C, nos s 1: Transmission in Propris and Analysis Mark Rodwll Univrsiy of California, Sana Barbara rodwll@c.ucsb.du , fax

2 Transmission in Analysis class nos, M. Rodwll, copyrighd 9 Gomris Characrisic Impdancs Tim Domain Analysis aic Diagrams Frquncy Domain analysis Rflcion cofficins Movmn of Rfrnc Plan Impdanc vs Posiion Smih Char Sanding Wavs Solving wav quaions quickly

3 class nos, M. Rodwll, copyrighd 9 yps of ransmission lins

4 Transmission ins for On-Wafr Wiring class nos, M. Rodwll, copyrighd 9 microsrip lin gomry volags currns W + I H I W+S coplanar wavguid W + I I I H

5 Transmission ins for On-Wafr Wiring class nos, M. Rodwll, copyrighd 9 gomry volags currns coplanar srips W+S I I W + - H slolin G + - I I H

6 Subsra Microsrip in class nos, M. Rodwll, copyrighd 9 W Dominan Transmission mdium in III- microwav & mm-wav ICs H Ky advanag: IC inrconncs hav vry low ground-lad inducanc Ground-lad inducanc: -lads o ground-bounc -is Millr-muliplid by IC gain Ky problms: hrough-wafr grounding hols vias coupling o TM mods in subsra ia inducanc forcs progrssivly hinnr wafrs a highr frquncis.

7 class nos, M. Rodwll, copyrighd 9 basic hory, C, o, vlociy, Gamma

8 Transmission ins class nos, M. Rodwll, copyrighd 9 A pair of wirs wih rgular spacing, dilcric loading along h lngh. Ths hav inducanc pr uni lngh and capacianc pr uni lngh. Forward and rvrs wavs propaga. Rflcions will occur if lins ar no corrcly rminad

9 Transmission ins: Basic Thory class nos, M. Rodwll, copyrighd 9 s d gn From basic nodal analysis of lin : d d di d and di d Cd C d d from which w find, v v I, o v o v whr o C and v 1 C

10 class nos, M. Rodwll, copyrighd 9 Forward and Rvrs Wavs currn in rvrs wav currn in forward wav volag in rvrs wav volag in forward wav o o v v v v

11 lociy and Characrisic Impdanc class nos, M. Rodwll, copyrighd 9 o C and v 1 C and C ar hr quaniis pr uni lngh. v c whr c is hspd of ligh and r, ff r, ff is h ffciv dilcric consan of h lin

12 Rflcions class nos, M. Rodwll, copyrighd 9 s gn A nd of and T s l s lin : T o whr A bginning of lin : o s s gn l l l whr s o o 1 1 s s o o 1 1 Nd good rminaions o prvn lin rflcions and ringing

13 class nos, M. Rodwll, copyrighd 9 Toal inducanc & capacianc in a lngh of lin If oallin lngh is C lngh lngh o o l l lngh Thn oalcapacianc in ha lngh is and oalinducanc in ha lngh is whr l lngh v "spd of ligh dlay"on hlin

14 class nos, M. Rodwll, copyrighd 9 umpd modls of vry shor ransmission lins T-modl Pi-modl C C C If oallin lngh or oallin dlay l is much lss han a wavlngh v is much lss han 1 or oallin dlay is much lss han puls risim hn h lin can b approximad as a T or scion C lngh lngh o o l lngh lngh f signal

15 class nos, M. Rodwll, copyrighd 9 addr modls of modraly shor ransmission lins Pi-modl synhsis C C C C C C C C C C T-modl synhsis C C C C C Clarly, w can brak a lin of any lngh ino scions of lngh l lin such ha lin l lin v is much lss han a signal priod. In his fashion a ransmission - lin can b modlld by an C filr. This is a frqun subsiuion in circui simulaions

16 Microsrip ins class nos, M. Rodwll, copyrighd 9

17 Microsrip in: Approxima Propris 1 class nos, M. Rodwll, copyrighd 9 W H Wid lin fild mosly in dilcric. This givs : v c 1 r H, whr c 1 is hspd of ligh 1 r W, whr is h fr spac wav impdanc no: wid lins hav problms

18 Microsrip in: Approxima Propris class nos, M. Rodwll, copyrighd 9 W H ~W +H If h lin is narrowr, hand analysis only Effciv widh W H approxima v r, ff H c lis 1 r, ff 1 r W H somwhr bwn ha of dpnding upon wha proporionof only vry appoximaly air and of h fild is h dilcric, in air.

19 class nos, M. Rodwll, copyrighd 9 ins in Tim Domain

20 aic Diagrams = Echo Diagrams class nos, M. Rodwll, copyrighd 9 Firs : Analyfor impuls rspons Thn : Us convoluion o find gnral rpons. Rcall : A nd of s whr A bginning of lin : T s gn lin : R R whr s o o 1 1 Rs o 1 o and Ts Rs o 1 o Rs

21 aic Diagrams = Echo Diagrams class nos, M. Rodwll, copyrighd 9

22 aic Diagrams = Echo Diagrams class nos, M. Rodwll, copyrighd 9 Now plas considr how h wavforms would chang if h gnraor wr a sp- funcion.

23 class nos, M. Rodwll, copyrighd 9 Rpad Rflcions Ringing or Exponnial Dcay If s is posiiv, pulsrsponssdcay gomrica lly xponnially If s is ngaiv, puls rsponssalso alrna in sign - -ringing. Bhavior appars vry clos o RC ringing. Why?

24 Tim-Domain Analysis class nos, M. Rodwll, copyrighd 9 C, Approxima modl R R s R nglc inducor RC circui charging. R s C

25 Tim-Domain Analysis class nos, M. Rodwll, copyrighd 9 C, Approxima modl R R s R nglc capacior R circui charging. R s C

26 Tim-Domain Analysis class nos, M. Rodwll, copyrighd 9 C, Approxima modl R C R C nglc nd capacior RC circui ringing S

27 class nos, M. Rodwll, copyrighd 9 and C ar imiing Cass of High-, low- lins C, High - lin : larg, small C. approximaly an inducor ow - lin : larg C, small. approximaly a capacior.

28 class nos, M. Rodwll, copyrighd 9 ins in Frquncy Domain

29 class nos, M. Rodwll, copyrighd 9 in Analysis in Frquncy Domain Smih Char Tim - domain analysis : inuiiiv and clar : pulss bouncing back and forh. vry difficul wih raciv,c load or gnraor impdancs Frquncy - domain analysis : lss inuiiiv. asy wihraciv,c load 1 sanding wavs Smih char or gnraor impdancs

30 class nos, M. Rodwll, copyrighd 9 in Analysis in Frquncy Domain: Phas Consan b Phasor noaion: s s cos o R, whr is o o is complx. Ona ransmission lin, wavs ravl as For a cosinusoidal wav ravling a vlociy v, cos v, v. v cos v cos b. b v is h phas propagaion consan.

31 class nos, M. Rodwll, copyrighd 9 in Analysis: Exponnial Wavs v v v v o b b - dircion : h ngaiv propagaing in wavs Exponnial h posiiv - dircion : propagaing in wavs Exponnial. wrin implicily as wavs ar sinusiodal, R cos Bcaus

32 class nos, M. Rodwll, copyrighd 9 olags on a Transmission in b b on hlin : Phasor volag implici. dpndnc im maks Working wih h phasor ] R[, on lin : olag

33 class nos, M. Rodwll, copyrighd 9 olags and Currns on a Transmission in I b b b b Phasor currn on hlin : on hlin : Phasor volag

34 Wav Paramrs class nos, M. Rodwll, copyrighd 9 Dfin wav ampliud a such ha if a 1, hn wav powr 1Wa. olag in forward wav : Currn in forward wav : I Powr in forward wav I * Foward wav ampliud: a Rvrs wav ampliud: b

35 class nos, M. Rodwll, copyrighd 9 Wav Paramrs and Powr w us R.M.S.quaniis. h nos, Throughou wav Powr in rvrs Powr in forward wav * * * * b b I a a I

36 Rlfcions from h oad class nos, M. Rodwll, copyrighd 9 whr and is -1 1 is h load rflcion cofficin. h* normalid * load impdanc.

37 Rlfcions from h Gnraor class nos, M. Rodwll, copyrighd 9 S T s s whr T S S is h sourc ransmission cofficin whr and S S S S S is -1 1 is h sourc rflcion cofficin. h* normalid * sourc impdanc. Noha h rfrnc plan has bn movd.

38 class nos, M. Rodwll, copyrighd 9 Movmn of Rfrnc Plan b b b b b bcaus 1 cofficin h posiion- dpndn rflcion is whr 1

39 Posiion-Dpndn Rflcion Cofficin Rflcion cofficin a a disanc l from load. l b class nos, M. Rodwll, copyrighd 9 Th rflcion cofficin has gon hrough a phasshif of l ngaiv radians. or ngaiv b l radians. or l ngaiv 36 dgrs....simply bcaus and undrgo 36 dgr phasshifs vry wavlngh of disanc.

40 class nos, M. Rodwll, copyrighd 9 Impdanc vs. Posiion 1 1 a any poin Normalid impdanc 1 1 Impdanc a any poin I I I

41 class nos, M. Rodwll, copyrighd 9 in Inpu Impdanc unnormali d. 1 1 normalid. 1 1 a impdanc Inpu l l l I l l l l l I l l l

42 class nos, M. Rodwll, copyrighd 9 Impdanc and Rflcion Cofficin vs Posion ool. Work wih a graphical bu dious mah. simpl, Concpually impdanc normalid cofficin s rflcion wavs I I b b b b b

43 Dvloping h Smih Char class nos, M. Rodwll, copyrighd 9 Th rlaionship is ky. Th rlaionship is a 1-1 mapping bwn h complx #s and ; a conformal ransformaion. This rlaionship can b graphd. In h - dimnsional plan of - h a rflcion hr, a rd do. cofficin is plan - rprsnd by a poin.

44 Moving Rfrnc Plans---on h Smih Char class nos, M. Rodwll, copyrighd 9 As w mov a disanc l away from h vcor roas by an angl h load, bl o l - 36 on whol roaion in h plan for ach half - wavlngh movmn on h ransmission lin.

45 Finding Impdancs class nos, M. Rodwll, copyrighd I 1 This is a 1: 1 rlaionship bwn rflcion cofficin magniud and phas and normalid impdanc ral and imaginary pars. Plo hunis of on h plan!

46 class nos, M. Rodwll, copyrighd 9 Finding Impdancs x x 1 3 x 3 R X r x x Ral and imaginary r 1 3 r 1 r 3 parsof impdanc x 13 can b rad from h curvd impdanc x 3 axs on h char. x 1

47 Finding Rflcion Cofficin Th magniud and angl of ar simply rad from h char radius and angl class nos, M. Rodwll, copyrighd 9 - plan his masurmn can b don using a rulr and a proracor*. *hough oday hcadsofawardos hmasurmn from a cursor.

48 Using h Smih Char class nos, M. Rodwll, copyrighd 9 Saring wih h load impdanc wcompu.,, W hn find his poin on hsmih char. This drmins cofficin. h load rflcion

49 Using h Smih Char class nos, M. Rodwll, copyrighd 9 W hn roa h vcor hrough an angl 36 o l. This locas cofficin. hinpu rflcion W can now rad off h inpu impdanc. in in l, l

50 Impdanc-Admianc Char class nos, M. Rodwll, copyrighd 9 Impdanc R X Normalid impdanc Admianc Y 1 G B Normalid impdanc Y Y r Y Y x g Smih chars can hav axs for, Y, or boh. o o o b

51 class nos, M. Rodwll, copyrighd 9 Solving Wav Equaions Quickly

52 class nos, M. Rodwll, copyrighd 9 Wavs and Fourir Transforms 1 y x x x y k y k x k x x y x y x E y x E k k E E E y x E E E E E J J E E b,,, wriing 's ar complx : h Somims,, and hsam for,,, Tosolv his asily, assum. nuraliy assum charg, Assum nonro conduciviy, ar uniform and if wav quaion : us a giv M axwll's quaions 1

53 class nos, M. Rodwll, copyrighd 9 Wavs and Fourir Transforms sa sady h wav quaion in h sinusiodal This is whr simply This bcoms,, and hsam for,,, Givn, and hsam for w hav : So k k k k k E E E y x E E E E E E y E x E y x y k y k x k x x y x x x x x y x

54 class nos, M. Rodwll, copyrighd 9 Wavs and Fourir Transforms 3 Y I I I I Y I I paralll sris paralll sris and Thn, and, Tosolv his asily, assum and sysmransmission - lin Now considr a 1- dimnsional

55 Wavs and Fourir Transforms 4 class nos, M. Rodwll, copyrighd 9 sris I and I Y paralll Muliply hs : I sris Y paralll I sris Y paralll Divid hs: I sris I Y paralll I sris Y paralll Th bfor h roo indicas ha hforward currn has hsam sign as h forward volag, whil h rvrs currn has sign opposiha of h rvrs volag.

56 Wavs and Fourir Transforms 5 class nos, M. Rodwll, copyrighd 9 in has sris inducanc and sris R rsisranc pr uni lngh. in has paralll capacianc C and paralll conducanc G pr uni lngh. Thn sris R Y paralll G C So : R G C R G C

57 class nos, M. Rodwll, copyrighd 9 Wavs and Fourir Transforms 6 in S- paramr calibraion somims Imporan slighly complx. bcoms No ha Us1. and Suppos C G R C C G R C O N C G R C G R C G R N

58 class nos, M. Rodwll, copyrighd 9 Wavs and Fourir Transforms 7 b C G R C C G C R C G R C C G R C O N C G R C G R C G R N Us 1. and Suppos